In the fabrication of integrated circuits, layers of semiconductor devices are patterned using lithography and etch processes. Both of these processes distort the pattern. The pattern on the photomask can be changed in order to compensate for the combined distortion of lithography and etch processes. The photomask data set describes a pattern PMASK DATA which comprises a union of polygons. The photomask data set is transferred on to the wafer, to form the pattern PWAFER, by a composition of pattern transformations:PWAFER=TETCH(TLITHO(TMASK(PMASK DATA)))  (1)TMASK is a transformation that maps the photomask data set to a pattern that is etched into a layer on the photomask. TMASK includes effects of software calculated dose adjustments, electron or laser beam interaction with a e-beam resist or a photoresist on the photomask, resist blur, development of the resist, and etching of the photomask.
TLITHO is a transformation that maps the pattern etched on the photomask to a pattern that is formed in a photoresist layer deposited on a wafer. TLITHO includes the effects of optical image formation, photo-reactions and catalytic reactions in the photoresist, dissolution of the photoresist in a developer solution.
TETCH is a transformation that maps the pattern that is formed in the photoresist on a wafer to the pattern that is etched in a layer underlying the photoresist. TETCH includes all steps of the etch process, such as resist-trim and hard-mask-open processes of gate-etch. Gate poly-silicon etch is usually preceded by etching of a silicon dioxide or silicon oxi-nitride hard mask.
Beale et al. (SPIE Vol. 5040, p. 1202-1209, 2003), which is incorporated herein by reference, proposed compensating the photomask data in multiple stages according to:PMASKDATA=TMASK−1(TLITHO−1(TETCH−1(PTARGET)))   (2)In equation (2), PTARGET is the pattern desired on the wafer, TETCH−1 is the inverse of the transformation TETCH, and TLITHO−1 is the inverse of the transformation TLITHO. The method of Equation (2) is also called multi-step process proximity correction (PPC) (see: Choi et al., Proc SPIE, Vol 5040, p. 1176, 2003, which is incorporated herein by reference). The process is called multi-step or tandem correction because it performs a sequence of inverse transformations. The method first starts with the final target pattern PTARGET and obtains the target for the lithography inversion, which is TETCH−1 (PTARGET). It then proceeds to find the target for the mask writing, which is TLITHO−1 (TETCH−1 (PTARGET)).
According to one approach, both PTARGET and TETCH−1 (PTARGET) are represented by a collection of polygons. However, representing TETCH−1 (PTARGET) by polygons is counter productive because etch correction results in segmentation and movement of edges of the polygons in PTARGET which results in a lithography target that is not lithography friendly. That is, TETCH−1 (PTARGET) obtained using such an approach is not in the range-space of the transformation TLITHO. Such an approach runs the risk of creating edge segments that are either too small or not optimal for lithography. It is among the objects of the present invention to address these and other limitations of prior art approaches, and to improve photomask fabrication.